Starting from the recursion (REF ) and using an approach similar to that of [1]}, [2]}, we can show that the weighted variance relation of the NLMS weight error vector results inHere, \({\bf u}_i\)  has diagonal correlation matrix \(\mbox{$\Lambda $}\)  and \({\bf q}_i\)  has rotated correlation matrix \({\bf R}_{\bar{q}}\) .
\(E[||{\tilde{\bf w}}_{i}||^2_{\mbox{$\sigma $}}]=E[||{\tilde{\bf w}}_{i-1}||^2_{{\bf F}\mbox{$\sigma $}}]+\mu ^2\sigma _v^2E\left[\frac{||{\bf u}_i||^2_{\mbox{$\sigma $}}}{(||{\bf u}_i||^2)^2}\right]+E[||{\bf q}_i||^2_{{\bf F}\mbox{$\sigma $}}],\) 
